Death of entanglement and purity in a two qubits–field system induced by phase damping

We investigate the death of entanglement and the purity loss of a two qubits–field system in the dispersive regime with a reservoir. For an alternative entanglement measure, we calculate the negativity of the eigenvalues of a partially transposed density matrix and compare it with the mutual entropy. A new measure related to the mutual entropy, namely, the index of entropy, is proposed to measure the degree of entanglement, and this agrees well with the negativity. We found that the entanglement has a strong sensitivity to the phase damping. The asymptotic behavior of the field states, the two qubits, and the total system fall into a mixed state. We treat the phenomena of death of entanglement and purity as they arise from the effect of phase damping.     

Noether——Lie symmetry and conserved quantities of mechanical system in phase space

In this paper, a new kind of symmetry and its conserved quantities of a mechanicalsystem in phase space are studied. The definition of this new symmetry, i.e. aNoether--Lie symmetry, is presented, and the criterion of this symmetry is alsogiven. The Noether conserved quantity and the generalized Hojman conserved quantityof the Noether--Lie symmetry of the system are obtained. The Noether--Lie symmetrycontains the Noether symmetry and the Lie symmetry, and has more generalizedsignificance.     

Geometric model of a fullerene molecule in the presence of Aharonov–Bohm flux

In this study, we describe a geometric model of a fullerene molecule with Ih symmetry. We combine the well known non-Abelian monopole approach and the geometric theory of defects, where every topological defect is associated with curvature and torsion, to describe a fullerene molecule. The geometric theory of defects in solids is used to consider the topological defects that allow this molecule to form and we apply a continuum formulation to describe this spherical geometry in the presence of an external Aharonov–Bohm flux. We solve a Dirac equation for this model and obtain the eigenvalues and eigenfunction of the Hamiltonian, and we obtain the persistent current for this model and show that it depends on the geometrical and topological properties of the fullerene.     

Two-dimensional quantum ring in a graphene layer in the presence of a Aharonov–Bohm flux

In this paper we study the relativistic quantum dynamics of a massless fermion confined in a quantum ring. We use a model of confining potential and introduce the interaction via Dirac oscillator coupling, which provides ring confinement for massless Dirac fermions. The energy levels and corresponding eigenfunctions for this model in graphene layer in the presence of Aharonov–Bohm flux in the centre of the ring and the expression for persistent current in this model are derived. We also investigate the model for quantum ring in graphene layer in the presence of a disclination and a magnetic flux. The energy spectrum and wave function are obtained exactly for this case. We see that the persistent current depends on parameters characterizing the topological defect.     

Geometric phase of a classical Aharonov–Bohm Hamiltonian

We present a gauge-invariant approach for associating a geometric phase with the phase space trajectory of a classical dynamical system. As an application, we consider the classical analog of the quantum Aharonov–Bohm (AB) Hamiltonian for a charged particle orbiting around a current carrying long thin solenoid. We compute the classical geometric phase of a closed phase space trajectory, and also determine its dependence on the magnetic flux enclosed by the orbit. We study the similarities and differences between this classical geometric phase and the AB phase acquired by the wave function of the quantum AB Hamiltonian. We suggest an experiment to measure the geometric phase for the classical AB system, by using an appropriate optical fiber ring interferometer.     

Transformation of general astigmatic Gaussian beams in a four-dimensional phase space

A phase space model of two-dimensional (2D) Gaussian beam propagation is generalized for three-dimensional (3D) general astigmatic Gaussian beam passing through first-order optical system. The general astigmatic Gaussian beam is represented by a four-dimensional (4D) phase super-ellipsoid that defined by an associated 4×4 real matrix, then the transformation formula of the phase super-ellipsoid of the beam through first-order optical system is derived. In particular, in the phase space framework, the beam propagation factor M2 value is proved to be a ratio of phase area of real beam to ideal beam, and a novel approach for a qualitative examination of the properties of fractional Fourier transform (FRT) for the beam is also provided.     

Quantum motion of a point particle in the presence of the Aharonov–Bohm potential in curved space

The nonrelativistic quantum dynamics of a spinless charged particle in the presence of the Aharonov–Bohm potential in curved space is considered. We chose the surface as being a cone defined by a line element in polar coordinates. The geometry of this line element establishes that the motion of the particle can occur on the surface of a cone or an anti-cone. As a consequence of the nontrivial topology of the cone and also because of two-dimensional confinement, the geometric potential should be taken into account. At first, we establish the conditions for the particle describing a circular path in such a context. Because of the presence of the geometric potential, which contains a singular term, we use the self-adjoint extension method in order to describe the dynamics in all space including the singularity. Expressions are obtained for the bound state energies and wave functions.     

An investigation of the gate dependence in an electronic Aharonov–Bohm interferometer

In this study we have obtained the dependence of the electronic distribution on the gate shape and the applied gate voltage in a quantum Hall effect based Aharonov–Bohm interferometer using a method presented in our previous studies. We have discussed the relation between the distribution of incompressible strips and observation of Aharonov–Bohm oscillations. We have obtained the distributions of the incompressible strips for various gate voltages and have shown that a gate potential sweep and a magnetic field sweep would be equivalent. Our calculations also predict that for wider gate separations it is possible observe a silent region while sweeping the magnetic field or the gate voltage.     

On a relation of the angular frequency to the Aharonov–Casher geometric phase in a quantum dot

By analysing the behaviour of a neutral particle with permanent magnetic dipole moment confined to a quantum dot in the presence of a radial electric field, Coulomb-type and linear confining potentials, then, an Aharonov–Bohm-type effect for bound states and a dependence of the angular frequency of the system on the Aharonov–Casher geometric phase and the quantum numbers associated with the radial modes, the angular momentum and the spin are obtained. In particular, the possible values of the angular frequency and the persistent spin currents associated with the ground state are investigated in two different cases.     

Thermodynamical properties of graphene in noncommutative phase–space

We investigated the thermodynamic properties of graphene in a noncommutative phase–space in the presence of a constant magnetic field. In particular, we determined the behaviour of the main thermodynamical functions: the Helmholtz free energy, the mean energy, the entropy and the specific heat. The high temperature limit is worked out and the thermodynamic quantities, such as mean energy and specific heat, exhibit the same features as the commutative case. Possible connections with the results already established in the literature are discussed briefly.     

An Aharonov-Anandan phase gate in the sub-Hilbert space of a coupling flux qubits system

We study two flux qubits with a parameter coupling scenario. Under the rotating wave approximation, we truncate the 4-dimensional Hilbert space of a coupling flux qubits system to a 2-dimensional subspace spanned by two dressed states |01 and |10 . In this subspace, we illustrate how to generate an Aharnov-Anandan phase, based on which, we can construct a NOT gate (as effective as a C-NOT gate) in this coupling flux qubits system. Finally, the fidelity of the NOT gate is also calculated in the presence of the simulated classical noise.     

The Quantum Phase Problem: Steps Toward a Resolution

Defining the observable canonically conjugate to the number observable N has long been an open problem in quantum theory. The problem stems from the fact that N is bounded from below. In a previous work we have shown how to define the absolute phase observable || by suitably restricting the Hilbert space of x and p like variables. Here we show that also from the classical point of view, there is no rigorous definition for the phase even though it's absolute value is well defined.     

Charge qubits and limitations of electrostatic quantum gates

We investigate quantum dot arrays and their application to quantum computation. The arrays analyzed contain a total of a few operating electrons with constant tunneling between the dots. We construct quantum two-level systems near the ground state with a large energy separation to the remainder of the states and with the electrostatic interaction modeled within the capacitance matrix formalism. A set of representative examples is investigated numerically.     

The Projective Hilbert Space as a Classical Phase Space for Nonrelativistic Quantum Dynamics

The projective Hilbert space carries a natural symplectic structure which enables one to reformulate quantum dynamics as a classical Hamiltonian one. PACS: 03.65.Ta, 02.40.Yy, 45.20.Jj.     

An alternative description of gabor spaces and gabor-toeplitz operators

We show a representation of the spaces of Gabor transforms using the general decomposition method of Vasilevski. This provides an interesting characterization of a class of Gabor-Toeplitz operators and enables to obtain their representation formulae, Wick calculus and the commutativity of the algebra of such operators particularly simply.